ALE and multi-step methods
 

I would be grateful if someone could tell me if, when using a multi-step method, such as a 3-stage Runge-Kutta method, should movement of the grid be taken into account in all the steps, or only the final one. Thanks

Re: ALE and multi-step methods
 

is RK a multi step method???

as I know, it's a self-starting single step method.

for example, in two-step method like predictor-corrector, two previous time step solutions must be memorized. but in RK, only one is to be memorized.

the purpose of those several subsetps in RK is to eliminate some truncation errors. for example, 4th order RK only involves 2nd order operations but possess 4th order accuracy.

your question regarding ALE + Rk is very good. I guess, you only need consider motion of mesh once. I am sure such a treatment is legitimate though I am not sure its accuracy. you can try, anyway.